% some facts about US relations
mother(x,y).
mother(y,z).
brother(z,a).
sister(a,b).
mother(c,b).
wife(f,c).
father(d,z).
wife(e,d).


%1) we need basic facts to compute sex for the sake of a sister:
sex(X,male) :- husband(_,X).
sex(X,male) :- brother(_,X).
sex(X,male) :- father(_,X).
sex(X,male) :- wife(X,_).
sex(X,female) :- wife(_,X).
sex(X,female) :- sister(_,X).
sex(X,female) :- mother(_,X).
sex(X,female) :- husband(X,_).

% 2) we will need to know parentage

bio_parent(X,Y) :- mother(X,Y).
bio_parent(X,Y) :- father(X,Y).
bio_parent(X,Y) :- mother(Y,X),!,fail.
bio_parent(X,Y) :- father(Y,X),!,fail.

parent(X,Y) :- bio_parent(X,Y).

% 3) we need to know about siblings
bio_sibling(X,Y) :- sister(X,Y).
bio_sibling(X,Y) :- brother(X,Y).

sibling(X,Y) :- bio_sibling(X,Y).
sibling(X,X) :- !,fail.

% now we can add the inference rules:
% RULE 1: What an AUNT is:
aunt(Pers,Aunt) :- parent(Pers,Par), is_sister(Par,Aunt).
is_sister(Pers,Sis) :- sex(Sis,female), sibling(Pers,Sis).

%rule 2: Sibling commutativity
% cannot use:
%  sibling(Pers,Sib2) :- sibling(Pers,Sib), sibling(Sib,Sib2).
%but: we only care about the real siblings at first (rest will be
% automatically inferred), so:
sibling(Pers,Sib2) :- bio_sibling(Pers,Sib1), sibling(Sib1,Sib2).

%rule 3: shared parents:
sibling(Pers,Sib) :- parent(Pers,Par), parent(Sib,Par).

%rule 4: parent siblings:
sibling(Me, Pers) :- parent(Me, Par), sibling(Par, Pers).